Place the chicken, broth, onion, celery, bay leaves, peppercorns, 2 tbsp dill and 2 tbsp thyme in a large stockpot. Add enough water to cover the chicken and bring to a boil. Reduce heat and simmer 1 hour.

To make the crust, mix 3 cups of flour with 1 tbsp dill, 1 tbsp thyme and salt in a large bowl. Add shortening and mix well. Add water 1 tbsp at a time until dough is blended and slightly sticky. Set aside.

Drain the chicken and strain the stock, setting aside 2 cups. Remove the skin from the chicken and discard. Remove all the meat from the carcass and shred into bite-sized pieces. Place in a large bowl and set aside.

Heat the oven to 375 degrees. Roll out half of the dough until it is 1/2″ thick and line the bottom of a pie dish. Roll out the other half to 1/2″ thickness and set aside.

Melt the butter in a large pan and add the potatoes. Saute 4-5 minutes until they turn golden. Add the carrots and mushrooms and cook another 3 minutes. Add the peas and cook another 2 minutes. Add 5 tbsp flour, mix well with vegetables and cook 1 minute. Stir in milk and reserved chicken stock and bring to a simmer. Cook until thick and bubbly, stirring constantly.

Combine the chicken pieces and vegetable/gravy mixture and stir to combine. Pour into the prepared pie dish and top with remaining crust. Cut 2-3 steam vents in the top and bake for 35-40 minutes.